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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Circle packing coordinates for the moduli space of tori


Author: G. Brock Williams
Journal: Proc. Amer. Math. Soc. 139 (2011), 2577-2585
MSC (2010): Primary 52C26, 30F60
Published electronically: December 17, 2010
MathSciNet review: 2784827
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Abstract: We develop a set of natural coordinates $ (\alpha,\beta)$ on the moduli space of Euclidean tori using the combinatorial structure of circle packings. Surfaces with rational coordinates support Brooks packings, while surfaces with rational $ \alpha$ and irrational $ \beta$ coordinates support generalized Brooks packings with periodic singularities.


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Additional Information

G. Brock Williams
Affiliation: Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
Email: brock.williams@ttu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10690-1
PII: S 0002-9939(2010)10690-1
Keywords: Circle packing, moduli space
Received by editor(s): January 18, 2010
Received by editor(s) in revised form: July 3, 2010
Published electronically: December 17, 2010
Communicated by: Mario Bonk
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.